To find the quartile deviation of the daily wages of 7 persons given as 12, 7, 15, 10, 17, 19, and 25, we will follow these steps:
### Step 1: Arrange the data in ascending order
First, we need to arrange the daily wages in ascending order.
**Data:** 12, 7, 15, 10, 17, 19, 25
**Ascending Order:** 7, 10, 12, 15, 17, 19, 25
### Step 2: Determine the first quartile (Q1)
The first quartile (Q1) is the median of the first half of the data. Since we have 7 data points, the first half consists of the first 3 values.
**First Half:** 7, 10, 12
To find Q1, we take the median of these values:
- The median of 7, 10, 12 is 10.
Thus, **Q1 = 10**.
### Step 3: Determine the third quartile (Q3)
The third quartile (Q3) is the median of the second half of the data. The second half consists of the last 3 values.
**Second Half:** 15, 17, 19, 25
To find Q3, we take the median of these values:
- The median of 15, 17, 19, 25 is the average of the two middle values (17 and 19):
\[
Q3 = \frac{17 + 19}{2} = \frac{36}{2} = 18
\]
Thus, **Q3 = 18**.
### Step 4: Calculate the Quartile Deviation
The quartile deviation (QD) is calculated using the formula:
\[
QD = \frac{Q3 - Q1}{2}
\]
Substituting the values we found:
\[
QD = \frac{18 - 10}{2} = \frac{8}{2} = 4
\]
### Final Answer
The quartile deviation of the daily wages is **4**.
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